Saturday, 9 August 2014

combinatorics - Prove that frac100!50!cdot250inBbbZ



I'm trying to prove that :



100!50!250




is an integer .



For the moment I did the following :



100!50!250=515299100250



But it still doesn't quite work out .



Hints anyone ?




Thanks


Answer



(2n)!n!2n=2nk=1knk=1(2k)=nk=1(2k1)Z.


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